CRAN Task View: Psychometric Models and Methods
|Contact:||Patrick.Mair at wu.ac.at|
Psychometrics is concerned with the design and analysis of research and
the measurement of human characteristics. Psychometricians have also
worked collaboratively with those in the field of statistics and
quantitative methods to develop improved ways to organize and analyze
data. Since much functionality is already contained in base R and there
is considerable overlap between tools for psychometry and tools
described in other views, particularly in
we only give a brief overview of packages that are closely related to
Please let us know
if we have omitted
something of importance, or if a new package or function
should be mentioned here.
Item Response Theory (IRT):
package fits extended Rasch models, i.e. the ordinary
Rasch model for dichotomous data (RM), the linear logistic test model
(LLTM), the rating scale model (RSM) and its linear extension (LRSM),
the partial credit model (PCM) and its linear extension (LPCM) using
conditional ML estimation. Missing values are allowed.
also fits the simple RM. Additionally,
functions for estimating Birnbaum's 2- and 3-parameter models based on a
marginal ML approach are implemented as well as the graded response
model for polytomous data, and the linear multidimensional logistic
includes the multivariate two- and three-parameter
logistic models, confirmatory bifactor analysis, polytomous confirmatory and
exploratory item response models, and partially-compensatory item response
modeling in conjunction with other IRT models.
package provides functions to estimate the Nominal Response Model and the Nested Logit Model. Both are models to examine multiple-choice items and other polytomous response formats.
estimates IRT models under (1) multidimensionality assumption, (2) discreteness of
latent traits, (3) binary and ordinal polytomous items.
Conditional maximum likelihood estimation via the EM algorithm and
information-criterion-based model selection in binary mixed Rasch models are
implemented in the
package and the
package estimates mixture Rasch models, including the
dichotomous Rasch model, the rating scale model, and the partial credit model.
Item and ability parameters can be calibrated using the package
plink. It provides unidimensional and multidimensional methods
such as Mean/Mean, Mean/Sigma, Haebara,
and Stocking-Lord methods for dichotomous (1PL, 2PL and 3PL) and/or
polytomous (graded response, partial credit/generalized partial credit, nominal,
and multiple-choice model) items.
The multidimensional methods include the Reckase-Martineau method and
of the Haebara and Stocking-Lord method.
package calibrates the parameters for Samejima's
Continuous IRT Model via EM algorithm and Maximum Likelihood. It allows to
compute item fit residual statistics, to draw empirical 3D item category
response curves, to draw theoretical 3D item category response curves, and to
generate data under the CRM for simulation studies.
package contains several traditional methods to detect
DIF in dichotomously scored items. Both uniform and non-uniform DIF effects can
be detected, with methods relying upon item response models or not. Some methods
deal with more than one focal group.
provides a logistic regression framework for
detecting various types of differential item functioning (DIF).
package allows for computarized adaptive testing using
computes maximum likelihood estimates and
pseudo-likelihood estimates of parameters of Rasch models for polytomous
(or dichotomous) items and multiple (or single) latent traits. Robust
standard errors for the pseudo-likelihood estimates are also computed.
A multilevel Rasch model can be estimated using the package
with functions for mixed-effects models with crossed or
partially crossed random effects. Furthermore, infrastructure for
estimating tree-structured item response models of the GLMM family using
is provided in
Nonparametric IRT analysis can be computed by means if the
package. It includes an automated item selection algorithm,
and various checks of model assumptions. In relation to that,
performs the Forward Search for Mokken scale analysis. It detects outliers, it
produces several types of diagnostic plots.
package fits nonparametric item and option
characteristic curves using kernel smoothing. It allows for optimal selection of
the smoothing bandwidth using cross-validation and a variety of exploratory
allows the construction of exact Rasch model
tests by generating random zero-one matrices with given marginals.
Simple Rasch computations such a simulating data and joint maximum
likelihood are included in the
computes classification accuracy and consistency under
Item Response Theory. Currently, only works for 3PL IRT models (or 2PL or 1PL)
and only for independent cut scores.
provides a simple common interface to the
estimation of item parameters in IRT models for binary responses with three
different programs (ICL, BILOG-MG, and ltm, and a variety of functions useful
with IRT models.
package estimates cognitive diagnosis models (DINA, DINO and GDINA models) and the general diagnostic model with discrete and quasi-continuous multidimensional latent variables which also includes the multidimensional compensatory item response model.
Gaussian ordination, related to logistic IRT and also approximated as
maximum likelihood estimation through canonical correspondence analysis
is implemented in various forms in the package
Two additional IRT packages (for Microsoft Windows only) are available and
documented on the JSS site.
computes multilevel IRT models,
hierarchically built up likelihood for estimating a two-parameter normal
ogive model for responses and a log-normal model for response times.
Bayesian approaches for estimating item and person parameters by means of
are included in
MCMCpack. In addition, the
package allows for Bayesian IRT and roll call analysis.
package produces commands to drive the dot program
from graphviz to produce a
graph useful in deciding whether a set of binary items might have a latent
scale with non-crossing ICCs.
The purpose of the
package is to factor out logic and math
common to IRT fitting, diagnostics, and analysis. It is envisioned as core
support code suitable for more specialized IRT packages to build upon.
package can be used to examine classification
accuracy and consistency under IRT models.
Correspondence Analysis (CA):
comprises two parts, one for simple
correspondence analysis and one for multiple and joint correspondence
analysis. Within each part, functions for computation, summaries and
visualization in two and three dimensions are provided, including
options to display supplementary points and perform subset analyses.
Other features are visualization functions that offer features such as
different scaling options for biplots and three-dimensional maps using
the rgl package. Graphical options include shading and
sizing plot symbols for the points according to their contributions to
the map and masses respectively. A corresponding GUI is provided by the
Simple and canonical CA are provided by the package
allows for diffenrent scaling methods such as standard scaling, Benzecri scaling,
centroid scaling, and Goodman scaling. Along with well-known two- and three-dimensional
joint plots including confidence ellipsoids, it offers alternative plotting possibilities
in terms of transformation plots, Benzecri plots, and regression plots.
A GUI (Windows only) that allows the user to construct interactive Biplots is
offered by the package
Homogeneity analysis aka multiple CA and various Gifi extensions can be
by means of the
package. Hull plots, span plots, Voronoi
plots, star plots,
projection plots and many others can be produced.
Simple and multiple correspondence analysis can be performed using
contains an extensive set of
functions covering, e.g., principal components, simple and multiple,
fuzzy, non symmetric, and decentered correspondence
analysis. Additional functionality is provided at
fits predictive and symmetric
co-correspondence analysis (CoCA) models to relate one data matrix to
another data matrix.
Apart from several factor analytic methods
performs CA including supplementary row and/or
column points and multiple correspondence analysis (MCA) with
supplementary individuals, supplementary quantitative variables and
supplementary qualitative variables.
supports all basic ordination methods, including
non-metric multidimensional scaling. The constrained ordination methods
include constrained analysis of proximities, redundancy analysis, and
constrained (canonical) and partially constrained correspondence
Other extensions of CA and MCA which also generalize many common IRT
models can be found on the
Structural Equation Models, Factor Analysis, PCA:
Ordinary factor analysis (FA) is the package stats as function
factanal(). Principal component analysis (PCA) can be fitted with
svd(), preferred) as well as
for compatibility with
rotation methods for FA based on gradient projection algorithms
can be found in the package
GPArotation. The package
a non-graphical solution to the Cattell scree test. Some graphical PCA
can be found in the
package fits general (i.e., latent-variable) SEMs by
and structural equations in observed-variable models by 2SLS. Categorical
variables in SEMs can be accommodated via the
package implements a wider variety of estimators
for observed-variables models, including nonlinear simultaneous-equations
See also the
package, for partial least-squares estimation,
task view for graphical models and the
task view for other related packages.
can be used to estimate a large variety of
multivariate statistical models, including path analysis, confirmatory factor
analysis, structural equation modeling and growth curve models. It includes the
lavaan model syntax which allows users to express their models in a compact way
and allows for ML, GLS, WLS, robust ML using Satorra-Bentler corrections, and
FIML for data with missing values. It fully supports for meanstructures and
multiple groups and reports standardized solutions, fit measures, modification
indices and more as output.
package allows for complex survey structural equation modeling (SEM). It fits structural equation models (SEM) including factor analysis, multivariate regression models with latent variables and many other latent variable models while correcting estimates, standard errors, and chi-square-derived fit measures for a complex sampling design. It incorporates clustering, stratification, sampling weights, and finite population corrections into a SEM analysis.
A general implementation of a computational framework for latent variable
models (including structural equation models) is given in
package generalizes the framework to censored and
dichotomous variables via a probit link formulation.
fits structural equation models using partial
least squares (PLS). The PLS approach is referred to as soft-modeling technique
requiring no distributional assumptions on the observed data. PLS methods with
emphasis on structural equation models with latent variables are given in
which also includes
as a companion package
with approaches of segmentation trees in PLS path modeling.
is a package designed to aid in Monte Carlo simulations
using SEM (for methodological investigations, power analyses and much more).
is a package of add on functions that can aid in fitting
SEMs in R (for example one function automates imputing missing data, running
imputed datasets and combining the results from these datasets).
conducts tests of difference in fit for mean and
covariance structure models as in structural equation modeling (SEM).
performs factor analysis based on a genetic algorithm
for optimization. This makes it possible to impose a wide range of restrictions on
the factor analysis model, whether using exploratory factor analysis, confirmatory
factor analysis, or a new estimator called semi-exploratory factor analysis (SEFA).
FA and PCA with supplementary individuals and supplementary
can be performed using the
has some options for sampling from
the posterior for ordinal and mixed factor models.
package provides nonlinear PCA and, by defining sets,
correlation analysis (models of the Gifi-family).
Independent component analysis (ICA) can be computed using
A desired number of robust principal components can be computed with the
includes functions such as
for estimating the
appropriate number of factors/components as well as
for item clustering.
An interface between the EQS software for SEM and R is provided by the
estimation of a wide variety of advanced multivariate statistical models. It
consists of a library of functions and optimizers that allow you to quickly and
flexibly define an SEM model and estimate parameters given observed data. It is
available under this
package allows to automate latent variable
model estimation and interpretation using Mplus.
Multidimensional Scaling (MDS):
package provides the following approaches of
multidimensional scaling (MDS) based on stress
minimization by means of majorization: Simple smacof on symmetric
smacof for rectangular matrices (unfolding models), smacof with constraints
on the configuration,
three-way smacof for individual differences (including constraints for
idioscal, indscal, and
identity), and spherical smacof (primal and dual algorithm). Each of these
implemented in a metric and nonmetric manner including primary, secondary,
and tertiary approaches
for tie handling.
package provides a multiway method to decompose a
tensor (array) of any order, as a generalisation of SVD also supporting
non-identity metrics and penalisations. 2-way SVD with these extensions
is also available. Additionally, the package includes some other
multiway methods: PCAn (Tucker-n) and PARAFAC/CANDECOMP with extensions.
and stats provide
functionalities for computing classical MDS using the
function. Sammon mapping
and non-metric MDS
are other relevant functions.
Non-metric MDS can additionally be performed with
provide the function
and some routines can be found in
Principal coordinate analysis can be computed with
Individual differences in multidimensional scaling can be computed with
allows for the computation of maximum likelihood
difference scaling (MLDS).
Classical Test Theory (CTT):
package can be used to perform a variety of tasks and
associated with classical test theory: score multiple-choice responses,
perform reliability analyses,
conduct item analyses, and transform scores onto different scales.
Functions for correlation theory, meta-analysis (validity generalization),
reliability, item analysis, inter-rater reliability, and classical utility are
contained in the
package calculates and plots the step-by-step
Cronbach-Mesbach curve, that is a method, based on the Cronbach alpha
coefficient of reliability, for checking the unidimensionality of a measurement
Cronbach alpha, kappa coefficients, and intra-class correlation coefficients
(ICC) can be found in the
A number of routines for scale construction and reliability analysis useful
for personality and experimental psychology are contained in the
Knowledge structure analysis:
provides functions and example datasets for the
psychometric theory of knowledge
spaces. This package implements data analysis methods and procedures for
simulating data and
transforming different formulations in knowledge space theory.
package contains basic functionality to generate, handle,
and manipulate deterministic knowledge structures based on sets and relations.
Functions for fitting probabilistic knowledge structures are included in the
Other related packages:
provides an infrastructure for psychometric
modeling such as data classes (e.g., for paired comparisons) and basic model
fitting functions (e.g., for Rasch and Bradley-Terry models).
Recursive partitioning based on psychometric models, employing the general
MOB algorithm (from package party) are implemented in
Currently, only Bradley-Terry trees are provided.
Psychometric mixture models based on flexmix infrastructure are provided by
means of the
package (at the moment Rasch mixture models
and Bradley-Terry mixture models).
package contains functions for non-IRT equating under
both random groups and nonequivalent groups with anchor test designs. Mean,
linear, equipercentile and circle-arc equating are supported, as are methods for
univariate and bivariate presmoothing of score distributions. Specific equating
methods currently supported include Tucker, Levine observed score, Levine true
score, Braun/Holland, frequency estimation, and chained equating.
package contains several IRT and non-IRT based
statistical indices proposed in the literature for detecting answer copying on
Latent class analysis with random effects can be performed with the package
In addition, the package
provides the function
lca(). Another package is
for polytomous variable latent class analysis.
package allows for the computation of simple,
stepwise configural frequency analysis (CFA).
Coefficents for interrater reliability and agreements can be computed with
generates design matrices for analysing real paired
comparisons and derived paired comparison data
(Likert type items / ratings or rankings) using a loglinear approach. Fits
loglinear Bradley-Terry model (LLBT) exploting an eliminate feature. Computes
for paired comparisons, rankings, and ratings. Some treatment of missing
values (MCAR and MNAR).
Bradley-Terry models for paired comparisons are implemented in the package
eba. The latter allows for the computation of
Psychophysical data can be analyzed with the
package contains functions to estimate the contribution of the n
scales to the judgment by a maximum likelihood method under several hypotheses
of how the perceptual dimensions interact.
Functions and example datasets for Fechnerian scaling of discrete object
sets are provided by
fechner. It computes Fechnerian
distances among objects representing subjective dissimilarities, and other
package provides functions for nonparametric
estimation of a psychometric function and for estimation of a derived threshold
and slope, and their standard deviations and confidence intervals.
Confidence intervals for standardized effect sizes: The
Functions for data screening, testing moderation, mediation, and estimating
power are contained in the
package can be used to visualize data as networks.
Social Relations Analyses for round robin designs are implemented in the
package. It implements all functionality of the SOREMO
software, and provides new functions like the handling of missing values,
significance tests for single groups, or the calculation of the self enhancement
Fitting and testing multinomial processing tree models, a class of statistical
models for categorical data with latent parameters, can be performed using the
package. These parameters are the link probabilities of a
tree-like graph and represent the cognitive processing steps executed to arrive
at observable response categories.The
package provides a
user-friendly way for analysis of multinomial processing tree (MPT) models.
Beta regression for modeling beta-distributed dependent variables, e.g., rates
is available in